Strong secrecy and decoding performance analysis for robust broadcasting under channel uncertainty

The compound broadcast channel with confidential messages is studied, where the transmitter sends a common message to two receivers and, at the same time, a confidential message to one receiver which has to be kept secret from the other one. It is only known to the transmitter and receivers that the actual channel realization is fixed and from a pre-specified set of channels. The information theoretic criterion of strong secrecy is analyzed in detail and generalized in such a way that it completely captures the behavior and the abilities of the non-legitimate receiver. Its impact on the decoding performance of the non-legitimate receiver is characterized as well. In particular, it is shown that regardless of the computational capabilities and the applied decoding strategy of the non-legitimate receiver, his decoding error always tends to one. This gives a valuable signal processing implication of the generalized secrecy criterion and identifies desirable properties of an optimal code design.